Date: Mar 18, 2004 11:03 PM
Author: Tim Brauch
Subject: Re: Hex Win Proof?
firstname.lastname@example.org (Bill Taylor) wrote in
> It is an old theorem that in Hex, once the board has been completely
> filled in with two colours, there *must* be a winning path for one
> or other of them.
> Now, I can prove this easily enough mathematically, but I'm wondering
> if there is a simple proof, or proof outline, that would be
> understandable and reasonably convincing to the intelligent layman.
> Can anyone help out please?
Here's what I'm thinking...
Suppose you have red going top-bottom and blue going left-right. If red
does not win, then there must be a path that divides the board into to
pieces, a top and a bottom piece. Red cannot be in any position in that
path, so it must be blue. Thus blue wins. Rotate pi/2 and switch colors.
Timothy M. Brauch
Department of Mathematics
Wake Forest University
news (dot) post (at) tbrauch (dot) com